Optimal Selling Mechanisms with Endogenous Seller Outside Offers

We examine a two-stage selling mechanism design problem, where the buyer makes her report and the seller endogenously decides his effort (hidden investment) to generate a possibly better outside offer. The optimal mechanism shows that the seller’s effort depends on the reported value of the buyer; a higher value lowers the seller’s incentive to invest in the outside offer. After the price of the outside offer is realized, if the buyer’s virtual value is less than the price, the seller takes the outside offer, and a termination fee equal to the virtual value is paid to the buyer.